Analyzing the Effects of Tolls and Operating Costs

on Statewide Travel Patterns

Vishal Gossain Thomas A. Williams Joseph P. Savage Jr. Christopher E. Mwalwanda

OBJECTIVES

• Illustrate the application of the Generalized Cost Function (GCF) as a proxy to a toll diversion curve

• Investigate the use of Operating Costs in the GCF

• Highlight pros and cons of implementing the GCF for statewide modeling.

• The analysis presented here does not represent the WSA procedure for toll based revenue estimation.

MODEL USED

• Texas Statewide Analysis Model (Texas Department of Transportation)

• Four Step Travel Demand Model• Implemented in TransCAD using

GISDK programming

SALIENT FEATURES

288 COUNTIES COVERED (Including some outside Texas)

4600 Zones + 142 External Stations, 323,350 square miles more than 35 million population

106,000 miles of network, 54,500 links with over 1 billion VMT

Four Step Model

• 2030 horizon year chosen, base year data grown to 2030 based on TDC forecasts and disaggregated.

• Passenger Trip Generation: TripCAL5

• Passenger Trip Distribution: ATOM2

• Passenger Mode Choice: Nested logit

Four Step Model

• Freight Trip Generation using regression equations developed based on Reebie and WEFA

• Freight Trip Distribution: ATOM2 • Mode Choice: Logit

Assignments

• All or Nothing Assignment • STOCH Assignment• Incremental Assignment• Capacity Restraint• User Equilibrium• Stochastic User Equilibrium • System Optimum Assignment

User Equilibrium Assignment

• TransCAD Multi Modal Multi Class Assignment utilized.

• All travelers have identical perceptions of time and cost.

• Equilibrium problem: No traveler can reduce his/her travel time by switching to another path (Wardrop conditions)

User Equilibrium Equation

0

0

..

min0

rij

a

ijr

rij

rij

ar

i j rija

a

v

a

x

v

Tx

networktheinalinksallforxvts

dxxsa

Dummy variable

Number of vehicles from i to j

Generalized Cost Function

Implementation

Compute shortest paths for every O-D minimizing GC (Solcurr)

Assign all O-D trips to shortest path (Soltemp)

Solcurr = (1-λ) Solcurr + λ Soltemp , λ chosen to minimize new

objective function (Frank-Wolfe algorithm)

Solution converged?

Compute GC for each link using seed values (Free flow times)

Compute GC for each link with new solution

No

Terminate

Yes

Crux of Equilibrium: VDF function

• Bureau of Public Records Function

i

i

iii C

xt

1

Free Flow Time

Capacity

Crux of Equilibrium: VDF function

• Conical Volume Delay Function

1,22

12

112)( 22

2

andC

Vxwhere

c

x

c

xxf

A Generalized Cost Delay Function

OD

mOD

mAi Mm

im

maamaa

mmOD MTFTxPCEctVDFVOTgc ,..,,.

Value of Time for mode m

Passenger Car Equivalent

Volume Delay Function

Toll for Section i and mode m

Toll Sensitivity

• What is the current and anticipated demand in the corridor?

• Toll Sensitivity as a proxy to potential demand

• How to incorporate sensitivities related to willingness to pay operating cost ?

• Value of Time• Operating Costs• Volume Delay Curves – Travel

Time Savings (Urban vs. Rural)

Key Variables

Toll Corridor

Toll Corridor

Toll Corridor

• A high speed (>=80 mph) competing toll corridor

• Separate Auto only (6 lanes) and Truck only Routes (4 lanes)

• Separate Toll Rates for Auto and Truck

• Limited Access (provided to only FM and above category roadways)

Value of Time for Auto

• Urban versus Intercity Markets• Income / Wage Rate Distribution• Rural / Purpose Segmentation

and Distribution• Average 10-12 cents per minute

($7.2 per hour) for rural interstate travel in 2005 dollars

Variations in Value of Time for Auto

$0

$2

$4

$6

$8

$10

$12

$14

$16

$18

Auto

Austin

DFW

El Paso

TTI per Auto

TTI per Person

20

04

Va

lue

of

Tim

e p

er

Ho

ur

$0

$5

$10

$15

$20

Austin

HBW HBS HBSCH HBO WBO OBO

20

04

Va

lue

of

Tim

e p

er

Ho

ur

Value of Time for Trucks

• Commercial Vehicle/Commodity Composition

• Fleet/Shipper versus Independent Operator

• Just-in-Time versus Flexible Scheduling

• Long versus Short Haul• $ 26.7 per hour• $ 17.4 - $ 22.6 per hour• $23.4 per hour based on logit model • Adopted Value of 42 cents per

minute ($25.2 per hour) in 2005 dollars

Operating Costs

• Helps to control utilization of unrealistic paths compared to a pure time based GC function

• Full Costs versus Perceived Costs

Operating CostsDirect Costs • Importance of fuel costs with the

current volatility in fuel prices.Indirect/Hidden Costs• Maintenance (tires, oil and other

work)• Unanticipated repairs• Depreciation in the value of the

vehicle• Depends on speed (magnitude and

duration)• Depends on pavement roughness

Operating Costs• 15.3 cents per mile

recommended for auto and 43.4 cents recommended for trucks

• City Driving conditions (19.1 cents and 52.9 cents respectively)

• Poor pavement quality (17.9 cents and 48.9 cents)

• All costs mentioned in 2003 dollars; 14 cents per mile for auto and 42 cents per mile for trucks used in 2005 dollars

Modeling Criteria

• Values of Time and Operating Costs based on overall market averages

• Toll rates set at 0 to 30 cents per mile

• UE Assignment, BPR VDF• Optimal number of iterations

and convergence criteria

Typical Toll Rates Ranges

$0.00

$0.05

$0.10

$0.15

$0.20

$0.25

$0.30

$0.35

$0.40

All Urban Rural Combination

Passenger Car Cash Rate per Mile 5-axle vehicle Cash Rate per Mile

Nationwide Toll Facilities Averages (USA - 75 Facilities)

2004

Cas

h T

oll R

ates

per

mile

Toll Sensitivity Curve (12 runs)

UE BPR

Sensitivities to Toll

Percentage of the total length of the corridor which has traffic more than 1000 vehicles for the considered toll rate

UE Assessment

• Fixed point equilibrium cut off• The same generalized cost

function for all links (toll or non toll)

• Perfect perception of time and costs along each route by all drivers.

Stochastic User Equilibrium

• No perfect information about network characteristics

• Different travel costs perception• Eliminates “zero volume” roads• Implemented in TransCAD

(utilizes Method of Successive Averages)

• Requires large number of iterations and hence a longer run time

Stochastic User Equilibrium

• Utility Maximization.• Random error term added to the

utility to mimic differences in perceived costs and imperfect information.

0

lE

IillVlU

i

iii

Randomly distributed error

Deterministic Utility

All influencing factors

Stochastic User Equilibrium

• Estimate probability

I

ii

i

kii

lP

IilP

IiIklUlUlP

1

1

10

,Pr

• Multinomial Logit, Multinomial Probit etc.

Stochastic User Equilibrium (8 runs)

Stochastic User Equilibrium

% length of corridor > 1000 volume

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.02 0.03 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36

Toll ($ per mile)

% o

f le

ng

th

UE Toll

SUE Toll

Conical Volume Delay

Function (12 runs) Comparison of different runs

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

50,000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Toll ($ per mile)

Vo

lum

e UE BPR

SUE

UE CONICAL

Conical Volume Delay Function

0.01 0.02 0.03 0.04 0.08 0.12 0.16 0.20.24

0.280.32

0.36

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

% of length

Toll ($ per mile)

% length of corridor with V>1000

UE BPR

SUE BPR

UE CONICAL

Operating Cost Analysis

Operating Cost Analysis

120,500,000

121,000,000

121,500,000

122,000,000

122,500,000

123,000,000

123,500,000

124,000,000

VMT

0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36

Operating Cost ($ per mile)

Operating Cost

Operating Cost Analysis

0.04 0.08 0.12 0.16 0.2 0.240.28

0.320.36

IH

US

SH

FMLocal

-6.0%

-4.0%

-2.0%

0.0%

2.0%

4.0%

6.0%

Operating Cost ($ per mile)

% change in VMT

Variation across functional class

IH

US

SH

FM

Local

SUMMARY

• Toll road modeling using statewide models has its limitations.

• Inclusion of operating costs is beneficial and requires further analysis.

• Different assignment techniques should be evaluated on a case by case basis.

• The analysis presented here does not represent the WSA procedure for toll based revenue estimation.

SUMMARY

• A single Generalized Cost function alone may not be adequate to capture the differences in the elasticity associated with tolls and travel times.

• Volume delay functions (reflecting adequate delay in urban vs rural areas) and GC function should be carefully considered and analyzed on a case by case basis.

QUESTIONS / COMMENTS

WILBUR SMITH ASSOCIATEShttp://www.wilbursmith.com